Question

A standard airline jet has 25,812 gallons of fuel and burns 4.2 gallons per mile. A jumbo airline jet has 31,311 gallons of fuel and burns 5.5 gallons of fuel per mile. How many miles (d) must each jet travel so they both have the same amount of fuel remaining?THERE IS 3 STEPS IN THE QUESTION

Answer 1

We will determine the fuel consumptions of each airline jet and compare them across the number of miled travelled.

It is given that the capacity of a standard airline jet in terms of fuel is as follows:

$\text{Capacity = 25,812 gallons}$

The standard airline jet burns fuel at a proportional rate with respect to the number of miles ( d ) travelled as follows:

$\text{Consumption = 4.2}\cdot d\text{ gallons}$

The amount of fuel remaining after travelling ( d ) miles can be expressed as follows:

$\text{Fuel Remaining ( Standard ) = Capacity - Consumption}$

Plug in the respective quantities and determine the amount of fuel left for the standard airline jet:

$\text{Fuel Remaining ( Standard ) = 25,812 - }4.2\cdot d$

Similarly, the capacity of the jumbo airline jet is expressed as follows:

$\text{Capacity = 31,311 gallons}$

The jumbo airline jet burns fuel at a proportional rate with respect to the number of miles ( d ) travelled as follows:

$\text{Consumption = 5.5}\cdot d\text{ gallons}$

The amount of fuel remaining after travelling ( d ) miles can be expressed as follows:

$\text{Fuel Remaining ( jumbo ) = Capacity - Consumption}$

Plug in the respective quantities and determine the amount of fuel left for the jumbo airline jet:

$\text{Fuel Remaining ( jumbo ) = 31,311 - 5.5}\cdot d$

Now we will compare the fuel remaining for both models of the jet for the distance ( d ) such that the fuel remaining for each jet is the same as follows:

$\text{Fuel Remaining ( Standard ) = Fuel Remaining ( jumbo )}$

Now plug in the respective expressions developed in previous steps above:

$25,812\text{ - 4.2}\cdot d\text{ = 31,311 - 5.5}\cdot\text{d}$

We have one equation expressed in the form one variable ( d ). We will perform the following algebra:

$\begin{gathered} 5.5d\text{ - 4.2d = 31,311 - 25,812} \\ 1.3\cdot d\text{ = 5,499} \\ \\ d\text{ = }\frac{5,499}{1.3} \\ \\ d\text{ = 4,230 miles} \end{gathered}$

Hence, the following answers are to be selected:

$\begin{gathered} \text{Step}1\colon\text{ amount of fuel in a standard airline jet = amount of fuel in a jumbo airline jet} \\ \text{Step2}\colon\text{ variable ( d ) represents the number of miles} \\ \text{Step}3\colon\text{ d = 4,230 miles} \end{gathered}$